And there are many more nowadays. If I could remember them, it still wouldn't be wise to post them all. As far as I know the turning torso started the craze, but I have absolutely no prove of that.

There a some different methods to get the twist. I havenīt seen a skyscraper with a entirely twisting structure. At least the core has to be straight. I then comes down to the outer shell. Make it such that it can handle the non-vertical forces, or make a non-loadbearing shell. Then revolving cantilevered floors form the twist. The Shanghai Tower has a hollow glass shell around a round tower around a square core.

Btw. I think it is mostly a stylistic way of "breaking out of the box". But I also heard once it is a method of breaking up wind forces in multiple directions, and therefore lessen peak forces. Can someone confirm this, or was that my imagination?

It refers to the freestanding columns on the groundlevel of a building. But I think it moreover refers to the concept of open space under that building. A space where nature, public space or traffic can flow unobstructed. Somewhat related to the much older arcade. But in itīs contemporary usage undoubtedly rooted in the theories of Corbusier.

Really tall towerlike skyscrapers structurally can't permit themselves huge open spaces, but it can be done. In wider blocks it even isn't uncommon.

I think the most elegant example of a tall building on pilotis is the Edifício Gustavo Capanema (1935-1943). It looks really monumental and comfortable at the same time, considering Rio's climate and the little park it is connected to. Designed by the team of Lucio Costaīs bureau. Oscar Niemeyer was actually an intern at Costa's office then but seemingly also had an influential role on the design (or people just can't imagine otherwise from the famous Niemeyer). The team invited le Corbusier to oversee the project.

Ah, I did not knew much examples of skyscrapers, but now I see the Seagram building is indeed a nice one. It not only has the pillars, it complements it with very clear glass and a white interior.

Piloti though is a very common architectural term, even in English. And it's usage is in skyscrapers does not really differ from that of lower buildings, just like 'plinth' and 'podium'. Besides, it refers to both the free-standing pillars and the space.

...talking about urban spaces and outer space. There are also a lot of skyscrapers build in ensembles of identical or semi-identical towers around an open space or plaza.

That space (or the ensemble of towers) could also be a category. I think the Rockefeller Center/Plaza would be the most famous example of that. But the former WTC would also be a good contender.